prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

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Using Theorem 6.1, prove that a line drawn through the mid

Click here👆to get an answer to your question ✍️ Using Theorem 6.1, prove that a line drawn through the mid - point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Question

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

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Updated on : 2022-09-05

Given:

Solution Verified by Toppr

In △ABC,D is midpoint of AB and DE is parallel to BC.

∴ AD=DB To prove: AE=EC Proof: Since, DE∥BC

∴ By Basic Proportionality Theorem,

DB AD ​ = EC AE ​ Since, AD=DB ∴ EC AE ​ =1 ∴ AE=EC

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Using Theorem 6.1, prove that a line drawn through the mid

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)

Solution:

We know that theorem 6.1 states that “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio (Basic Proportionality theorem)”.

Consider the diagram as shown below.

In ΔABC, D is the midpoint of AB

Therefore, AD = BD

AD/BD = 1 .......... (i)

Now, DE || BC

⇒ AE/EC = AD/BD [Theorem 6.1]

⇒ AE/EC = 1 [From equation (1)]

⇒ AE = EC

Hence, E is the midpoint of AC.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 6Video Solution:

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)

Class 10 Maths NCERT Solutions Chapter 6 Exercise 6.2 Question 7

Summary:

Hence it is proved that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side. Thus, E is the midpoint of AC.

☛ Related Questions:

Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO.

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.

In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)

स्रोत : www.cuemath.com

Ex 6.2, 7

Ex 6.2, 7 Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Rec..

Check sibling questions

Ex 6.2, 7 - Chapter 6 Class 10 Triangles (Term 1)

Last updated at March 16, 2023 by Teachoo

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Transcript

Ex 6.2, 7 Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX). Given: Let us assume ABC Where DE is parallel to BC & D is the mid point of AB To prove: E is the mid point of AC Proof: In ABC , DE II BC We know that if a line drawn parallel to one side of triangle, intersects the other two sides in distinct points, then it divides the other 2 side in same ratio / = / / = / 1 = / EC = AE E is the mid-point of AC Hence proved

Next: Ex 6.2, 8 →

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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